Solutions to some classical problems in linear elastostatics

2020 ◽  
pp. 145-212
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Cross Section ◽  
Function Method ◽  
Arbitrary Cross Section ◽  
Two Dimensional ◽  
Linear Elastic ◽  
Linear Elastostatics ◽  
Airy’S Stress Function ◽  
Elastic Fracture ◽  
Stress And Deformation ◽  
Stress Function Method

This chapter presents and discusses the solution of several classical problems in linear elastostatics, including thick-walled spheres and cylinders under external and internal pressure; bending and torsion of prismatic bars of arbitrary cross section; and the use of Airy’s stress function method to solve several two-dimensional plane strain and plane stress traction boundary value problems, including a demonstration of the extent of the Saint-Venant effect. The discussion also includes an analysis of the asymptotic stress and deformation fields near the tips of sharp cracks, and a discussion of stress intensity factors which are of importance in linear elastic fracture mechanics.

Two-dimensional problem of diffraction by dielectric cylinder of arbitrary cross-section in plane-layered medium. TheE-polarization case

1992 ◽  
Vol 34 (10-12) ◽  
pp. 914-921
Author(s):  
A. B. Vasil'ev ◽  
N. P. Zhuk ◽  
D. A. Rapoport ◽  
A. G. Yarovoi
Keyword(s):  
Cross Section ◽  
Layered Medium ◽  
Arbitrary Cross Section ◽  
Dielectric Cylinder ◽  
Two Dimensional ◽  
Dimensional Problem

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

Long waves in a uniform channel of arbitrary cross-section

1968 ◽  
Vol 32 (2) ◽  
pp. 353-365 ◽  
Author(s):  
D. H. Peregrine
Keyword(s):  
Solitary Wave ◽  
Cross Section ◽  
Gravity Waves ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Arbitrary Cross Section ◽  
Long Waves ◽  
Order Of Approximation ◽  
Two Dimensional ◽  
Uniform Channel

Equations of motion are derived for long gravity waves in a straight uniform channel. The cross-section of the channel may be of any shape provided that it does not have gently sloping banks and it is not very wide compared with its depth. The equations may be reduced to those for two-dimensional motion such as occurs in a rectangular channel. The order of approximation in these equations is sufficient to give the solitary wave as a solution.

Two-dimensional toroidal MHD equilibria of arbitrary cross-section

1983 ◽  
Vol 29 (1) ◽  
pp. 173-175 ◽  
Author(s):  
Ferdinand F. Cap
Keyword(s):  
Equilibrium Problem ◽  
Cross Section ◽  
Arbitrary Cross Section ◽  
Two Dimensional ◽  
New Approach ◽  
Mhd Equilibrium ◽  
Mhd Equilibria

A new approach to the solution of the MHD equilibrium problem is outlined.

Non-linear elastic non-uniform torsion of bars of arbitrary cross-section by BEM

2010 ◽  
Vol 45 (1) ◽  
pp. 63-74 ◽  
Author(s):  
E.J. Sapountzakis ◽  
V.J. Tsipiras
Keyword(s):  
Cross Section ◽  
Arbitrary Cross Section ◽  
Linear Elastic ◽  
Non Linear

A boundary element method for two dimensional linear elastic fracture analysis

1996 ◽  
Vol 74 (3) ◽  
pp. 219-251 ◽  
Author(s):  
Chungchu Chang ◽  
Mark E. Mear
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Fracture Analysis ◽  
Two Dimensional ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Element Method
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